How to retrieve missing vertices from STL file
Verify that you have not restricted painting to certain faces.  Blender has elaborate tools for restricting access.  Face Selection





Verify you have not hidden vertices with the letter H.  See the Blender Menus to Hide and Unhide.  This is in Edit Mode.  
Inspect a render to see if vertices are missing


After the above steps consider joining.


Be in object mode.
Make sure you select both objects, then join.  
Join of two or more [selected] mesh objects in [object mode] works.


Selection in Object Mode.  Select Multiple Objects


Shift Click.  
Letter B to rectangle select.
Letter C to select by the centers of objects.


I you have not invested too much time in painting consider starting fresh with the correct STL file. (Delete the damaged mesh) Maybe your painting skills are faster than vertex joining skills.

Joining the vertices in recovery mode seems a challenge.  Blender has many vertex fill tools.